Properties

Label 7.22
Level 7
Weight 22
Dimension 37
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 88
Trace bound 1

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 22 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(88\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_1(7))\).

Total New Old
Modular forms 45 41 4
Cusp forms 39 37 2
Eisenstein series 6 4 2

Trace form

\( 37 q + 573 q^{2} + 375783 q^{3} + 4028413 q^{4} - 43984971 q^{5} - 437011206 q^{6} + 1526574637 q^{7} + 746714415 q^{8} + 13746465405 q^{9} + O(q^{10}) \) \( 37 q + 573 q^{2} + 375783 q^{3} + 4028413 q^{4} - 43984971 q^{5} - 437011206 q^{6} + 1526574637 q^{7} + 746714415 q^{8} + 13746465405 q^{9} + 90177481662 q^{10} - 43716783531 q^{11} + 910206557274 q^{12} + 399488492144 q^{13} + 848963870265 q^{14} + 3130925336562 q^{15} - 4683081131663 q^{16} - 1904057113173 q^{17} - 60964738146813 q^{18} + 51354550968089 q^{19} - 393134429091264 q^{20} + 363593052067329 q^{21} - 252658560243132 q^{22} + 291348595233135 q^{23} + 167178461173698 q^{24} + 862764286589101 q^{25} - 2078830483051644 q^{26} + 518128564954782 q^{27} - 5937328148974523 q^{28} + 15905654081502882 q^{29} - 21158762322208746 q^{30} - 7775191845711799 q^{31} + 17900378850707823 q^{32} - 12342944227716489 q^{33} - 76792077088415586 q^{34} + 56467151698040433 q^{35} + 264500118210689337 q^{36} - 131468638614018553 q^{37} - 135451032405264168 q^{38} + 293005985985765234 q^{39} + 158473005475962000 q^{40} - 456382192116512466 q^{41} + 105657821963219862 q^{42} + 731934580095191624 q^{43} - 1198343917306781244 q^{44} - 1600436321701804170 q^{45} + 1963466951935565694 q^{46} - 513367999904463321 q^{47} - 1125974073687904002 q^{48} + 43535757658752037 q^{49} + 4729418610280239453 q^{50} - 1397783536995952257 q^{51} - 2438939626051234180 q^{52} - 2287853708087200569 q^{53} + 3142239796140891378 q^{54} - 3106685802362608758 q^{55} + 7817969266470032271 q^{56} - 3564193187046725910 q^{57} + 4453995029144130258 q^{58} + 14658457157054694195 q^{59} - 49910556141722121636 q^{60} - 8478125138445007495 q^{61} + 41747426947757636712 q^{62} - 8494499939359112973 q^{63} - 14860031429746710239 q^{64} + 24455143398658819434 q^{65} + 83162707716711226662 q^{66} + 225547483833782669 q^{67} - 77203274272326256782 q^{68} + 95816641086051465942 q^{69} - 103353696970170333414 q^{70} + 8235425234873700672 q^{71} + 52745046612099086271 q^{72} + 2975403789259589963 q^{73} - 212367189445276807632 q^{74} + 84076725471313093998 q^{75} - 112448187450094131118 q^{76} - 18772406240366775045 q^{77} - 200520408705474595584 q^{78} - 119107542133543644577 q^{79} - 133762090088230467792 q^{80} + 789411295999160319042 q^{81} + 324171779116462274718 q^{82} - 1055605704943108601142 q^{83} + 449604434161309356594 q^{84} + 985594503278134787970 q^{85} + 328224443935217922552 q^{86} - 1304148491381905296018 q^{87} + 1566147929114043753408 q^{88} - 402787912838956251357 q^{89} - 991772820595658783364 q^{90} + 470686498210687351460 q^{91} + 384178447600627018536 q^{92} - 1024112965921016190657 q^{93} + 153248663093425450434 q^{94} + 1782379668376303515417 q^{95} - 1815566478241427999934 q^{96} - 243516272898187227442 q^{97} - 5134855506236731137219 q^{98} - 722677163831457596100 q^{99} + O(q^{100}) \)

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_1(7))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
7.22.a \(\chi_{7}(1, \cdot)\) 7.22.a.a 5 1
7.22.a.b 6
7.22.c \(\chi_{7}(2, \cdot)\) 7.22.c.a 26 2

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_1(7))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_1(7)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 1}\)